The focal length of the eye lens increases when eye muscles
Question: The focal length of the eye lens increases when eye muscles (a)are relaxed and lens becomes thinner (b)contracts and lens becomes thicker (c)are relaxed and lens becomes thicker (d)contract and lens becomes thinner Solution: (a).Explanation :Focal length of thin lens is greater than the focal length of thick glass....
Read More →When light rays enter the eye,
Question: When light rays enter the eye, most of the refraction occurs at the (a)crystalline lens (b)outer surface of the cornea (c)iris (d)pupil Solution: (b)outer surface of the cornea...
Read More →Tick (✓) the correct answer
Question: Tick (✓) the correct answer: The price of watch including 10% VAT is Rs 825. What is its basic price? (a) Rs 742.52 (b) Rs 775 (c) Rs 750 (d) Rs 907.50 Solution: (c) Rs 750 Let the basic price be $x$. VAT $=10 \%$ of Rs $x$ $=\operatorname{Rs}\left(x \times \frac{10}{100}\right)$ $=\operatorname{Rs} \frac{x}{10}$ $\therefore$ Price including $\mathrm{VAT}=\mathrm{Rs}\left(\mathrm{x}+\frac{\mathrm{x}}{10}\right)$ $=R s . \frac{11 x}{10}$ Now, $\frac{11 \mathrm{x}}{10}=825$ $\quad \Right...
Read More →Water in deep sea is bluish in colour due to
Question: Water in deep sea is bluish in colour due to (a)absorption of light by the sea (b)reflection of sky in water (c)scattering of light (d)presence of plants in the sea. Solution: (c)scattering of light...
Read More →Which of the following phenomena contributes
Question: Which of the following phenomena contributes significantly to the reddish appearance of the sun at sunrise or sunset ? (a)Dispersion of light (b)Scattering of light (c)Total internal reflection of light (d)Reflection of light from the earth. Solution: (b). Explanation :Intensity of scattered light, I 1/4. Since the wavelength of red light is greater than the wavelengths of all other lights, therefore, red colour is scattered least and confined around the sun....
Read More →The clanger signals installed at the top of tall
Question: The clanger signals installed at the top of tall building are red in colour. These can be seen from a distance because among all other colours, the red light (a)is scattered the most by smoke or fog (b)is scattered the least by smoke or fog (c)is absorbed the most by smoke or fog (d)moves fastest in air Solution: (b). Explanation :Intensity of scattered light, I 1/4. Since the wavelengths of red light is greater than the wavelengths of all other lights, therefore, red colour can be see...
Read More →Tick (✓) the correct answer
Question: Tick (✓) the correct answer: The marked price of an article is 10% more than the cost price and a discount of 10% is given on the marked price. The seller has (a) no gain and no loss (b) 1% gain (c) 1% loss (d) none of these Solution: (c) 1% loss Let the CP be Rs 100 . Discount $=10 \%$ of $\mathrm{MP}$ Then, marked price $=$ Rs 110 $=(10 \%$ of Rs. 110$)$ $=$ Rs. $\left(110 \times \frac{10}{100}\right)$ $=$ Rs. 11 Now, $S P=(M P)-($ discount $)$ $\quad=R s(110-11)$ $\quad=R s 99$ $\th...
Read More →Find the domain of the function,
Question: Find the domain of the function, $f(x)=\log |x|$. Solution: $\log x$ function has domain $R^{+}$. When x is replaced by |x|, the function f shows value as $f(x)=\log (x) ; x0$ $=\log (-x) ; x0$ Hence in the function x cannot be zero as log function is not defined for x=0. Domain of f(x) is R {0}...
Read More →Differentiate the following functions with respect to x :
Question: Differentiate the following functions with respect to $x$ : $x^{x \cos x}+\frac{x^{2}+1}{x^{2}-1}$ Solution: Let $y=x^{x \cos x}+\frac{x^{2}+1}{x^{2}-1}$ $\Rightarrow y=a+b$ where $\mathrm{a}=\mathrm{x}^{\mathrm{x} \cos \mathrm{x}} ; \mathrm{b}=\frac{\mathrm{x}^{2}+1}{\mathrm{x}^{2}-1}$ $\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\mathrm{da}}{\mathrm{dx}}+\frac{\mathrm{db}}{\mathrm{dx}}$ $\left\{\right.$ Using chain rule, $\frac{d(u+a)}{d x}=\frac{d u}{d x}+\frac{d a}{d x}$ where $a$ and $u...
Read More →Which of the following statements is correct regarding
Question: Which of the following statements is correct regarding the propagation of light of different colours of white light in air ? (a)Red light travels fastest. (b)Blue light moves faster than green light. (c)All the colours of white light move with the same speed. (d)Yellow light moves with the mean speed as that of the red and the violet light. Solution: (c).Explanation :There is no dispersion of white light in air. So all colours travel with the same speed....
Read More →Tick (✓) the correct answer
Question: Tick (✓) the correct answer: A dealer lists his articles at 20% above cost price and allows a discount of 10%. His gain per cent is (a) 10% (b) 8% (c) 9 % (d) $8 \frac{1}{4} \%$ Solution: (b) 8% Let the CP be Rs 100 . Then, marked price $=$ Rs 120 Discount $=10 \%$ of $\mathrm{MP}$ $=(10 \%$ of Rs 120$)$ $=$ Rs. $\left(120 \times \frac{10}{100}\right)$ $=$ Rs. 12 Now, $\mathrm{SP}=(\mathrm{MP})-($ discount $)$ $=\mathrm{Rs}(120-12)$ $=\mathrm{Rs} 108$ Gain percentage $=(108-100) \%$ =8...
Read More →Find the range of the function,
Question: Find the range of the function, $f(x)=\frac{x}{|x|}$ Solution: |x| is defined as $|\mathrm{x}|=\mathrm{x} ; \mathrm{x}=0$ $-\mathrm{x} ; \mathrm{x}0$ $\frac{1}{|x|}=\frac{1}{x ;} \mathrm{x}0$ $=\frac{-1}{x} ; \mathrm{x}0$ $\frac{x}{|x|}=1 ; \mathrm{x}0$ $=-1 ; \mathrm{x}0$ Hence $f(x)$ gives output values 1 and $-1$ only. Range is $\{1,-1\}$....
Read More →The clear sky appears blue because
Question: The clear sky appears blue because (a)blue light gets absorbed in the atmosphere (b)ultraviolet radiations are absorbed in the atmosphere. (c)violet and blue lights get scattered more than lights of all other colours by the atmosphere. (d)light of all other colours is scattered more than the violet and blue colour lights by the atmosphere. Solution: (c). Explanation :Intensity of scattered light, I 1/4. The wavelength of blue and violet light is smaller than the wavelengths of other co...
Read More →Twinkling of stars is due to atmospheric
Question: Twinkling of stars is due to atmospheric (a)dispersion of light by water droplets (b)refraction of light by different layers of varying refractive indices. (c)scattering of light by dust particles (d)internal reflection of light by clouds. Solution: (b). Explanation :When sun light enters the earths atmosphere, it continuously goes from rarer to the denser medium and hence refraction of light takes place. The refraction of light taking place in the atmosphere is known as atmospheric re...
Read More →Tick (✓) the correct answer
Question: Tick (✓) the correct answer: If an article is sold at a gain of 5% instead of being sold at a loss of 5%, a man gets Rs 5 more. What is the cost price of the article? (a) Rs 50 (b) Rs 40 (c) Rs 60 (d) Rs 80 Solution: (a) Rs. 50 Let the $\mathrm{CP}$ be Rs $x$. Then, we have: $(105 \%$ of $x)-(95 \%$ of $x)=5$ $\Rightarrow\left(\frac{105}{100} \times x\right)-\left(\frac{95}{100} \times x\right)=5$ $\Rightarrow\left(\frac{105 x}{100}-\frac{95 x}{100}\right)=5$ $\Rightarrow \frac{(105 x...
Read More →Solve this
Question: If $f(x)=\frac{k x}{x+1}$, where $x \neq-1$ and $f\{f(x)\}=x$ for $x \neq-1$ then find the value of k. Solution: Given. $f(x)=\frac{k x}{x+1}, x \neq-1$ $F(f(x))=f\left(\frac{k x}{(x+1)}\right.$ $=\frac{k \frac{k x}{x+1}}{\frac{k x}{x+1}+1}$ $=\frac{k^{2} x}{k x+x+1}$ Given that f(f(x)) = x $\mathrm{x}=\frac{k^{2} \mathrm{x}}{k x+x+1}$ Dividing both sides by x $1=\frac{k^{2}}{k x+x+1}$ $\mathrm{kx}+\mathrm{x}+1=k^{2}$ $1^{k^{2}}-k x-(x+1)=0$ $\mathrm{k}=\frac{\frac{x+\sqrt{x^{2}+4 x+4}...
Read More →Which of the following phenomena of light
Question: Which of the following phenomena of light are involved in the formation of a rainbow ? (a)Reflection, refraction and dispersion (b)Refraction, dispersion and total internal reflection. (c)Refraction, dispersion and internal reflection. (d)Dispersion, scattering and total internal reflection Solution: (c). Explanation :When light falls on a droplet, refraction of light takes place. This refracted light suffers dispersion. Then the light suffer total internal reflection from other surfac...
Read More →At noon, the sun appears white as
Question: At noon, the sun appears white as (a)light is least scattered (b)all the colours of the white light are scattered away. (c)blue colour is scattered the most (d)red colour is scattered the most Solution: (a).Explanation :At noon, scattering of all colours is almost same....
Read More →Tick (✓) the correct answer
Question: Tick (✓) the correct answer: A man buys an article for Rs 150 and makes overhead expenses which are 10% of the cost price. At what price must he sell it to gain 20%? (a) Rs 182 (b) Rs 192 (c) Rs 198 (d) Rs 208 Solution: (c) Rs 198 $\mathrm{CP}=\mathrm{Rs} 150$ Total $\mathrm{CP}=\mathrm{Rs}(150+10 \%$ of 150$)$ $=\operatorname{Rs}\left(150+\left(\frac{10}{100} \times 150\right)\right)$ $=\operatorname{Rs}(150+15)$ $=\operatorname{Rs} 165$ $\therefore$ Desired $\mathrm{SP}=\left\{\frac...
Read More →A student wants to have third colour
Question: A student wants to have third colour from the top corresponds to the colour of the sky after the dispersion of white light through a glass prism. He placed prism ABC with BC as base as shown in figures P, Q, R and S. Which position of the prism is correct ? (a)P (b)Q (c)R (d)S. Solution: (b).Explanation :Colour of sky is blue....
Read More →Differentiate the following functions with respect to x :
Question: Differentiate the following functions with respect to $x$ : $x^{(\sin x-\cos x)}+\frac{x^{2}-1}{x^{2}+1}$ Solution: Let $y=x^{(\sin x-\cos x)}+\frac{x^{2}-1}{x^{2}+1}$ $\Rightarrow y=a+b$ where $a=x^{(\sin x-\cos x)} ; b=\frac{x^{2}-1}{x^{2}+1}$ $\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\mathrm{da}}{\mathrm{dx}}+\frac{\mathrm{db}}{\mathrm{dx}}$ $\left\{\right.$ Using chain rule, $\frac{\mathrm{d}(\mathrm{u}+\mathrm{a})}{\mathrm{dx}}=\frac{\mathrm{du}}{\mathrm{dx}}+\frac{\mathrm{da}}{\math...
Read More →A student sitting on the last bench can read
Question: A student sitting on the last bench can read the letters written on the black board but is not able to read the letters written in his test book. Which of the following statements is correct ? (a)The near point of his eyes has receded away (b)The near point of his eyes has come closer to him (c)The far point of his eyes has receded away (d)The far point of his eyes has come closer to him. Solution: (a). Explanation :Student suffers from hypermetropia. In this case, the near point of th...
Read More →Tick (✓) the correct answer
Question: Tick (✓) the correct answer: The profit earned on selling an article for Rs 625 is the same as loss on selling it for Rs 435. The cost price of the article is (a) Rs 520 (b) Rs 530 (c) Rs 540 (d) Rs 550 Solution: (b) Rs 530 Let the $\mathrm{CP}$ be Rs $x$. Then, we have:$625-x=\mathrm{x}-435$ $\Rightarrow x+x=625+435$ $\Rightarrow 2 x=1060$ $\therefore x=\operatorname{Rs} 530$...
Read More →A person cannot see distinctly objects kept beyond 2 m.
Question: A person cannot see distinctly objects kept beyond 2 m. This defect can be corrected by using a lens of power (a)+0.5 D (b)-0.5 D (c)+0.2 D (d)-0.2 D Solution: (b).Explanation :Person is suffering from myopia. Focal length of the lens used to correct the defect, f = d = 2 m $\therefore$ Power of lens, $\mathrm{P}=\frac{1}{f}=-\frac{1}{2 m}=-0.5 \mathrm{D}$...
Read More →Tick (✓) the correct answer
Question: Tick (✓) the correct answer: A man sold two chairs for Rs 500 each. On one he gains 20% and on the other he loses 12%. His net gain or loss per cent is (a) 1.5% gain (b) 2% gain (c) 1.5% loss (d) 2% loss Solution: (a) 1.5% gain SP of the first chair $=$ Rs 500 Gain percentage $=20 \%$ $\therefore \mathrm{CP}$ of the first chair $=\left\{\frac{100}{(100+\text { gain } \%)} \times \mathrm{SP}\right\}$ $=$ Rs. $\left\{\frac{100}{(100+20)} \times 500\right\}$ $=$ Rs. $\left(\frac{100}{120}...
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